Related papers: Spectral convergence of diffusion maps: improved e…

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically…

In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…

Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…

Diffusion models have recently outperformed alternative approaches to model the distribution of natural images, such as GANs. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space…

Purpose: In the present work we describe the correction of diffusion-weighted MRI for site and scanner biases using a novel method based on invariant representation. Theory and Methods: Pooled imaging data from multiple sources are subject…

We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…

Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a…

Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two…

Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral…

Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…